A Proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type
File(s)Inventiones mathematicae_2015.pdf (775.84 KB)
Accepted version
Author(s)
Cheraghi, D
Chéritat, A
Type
Journal Article
Abstract
Marmi Moussa and Yoccoz conjectured that some error function Upsilon, related to the approximation of the size of Siegel disk by some arithmetic function of the rotation number theta, is a Holder continuous function of theta with exponent 1/2. Using the renormalization invariant class of Inou and Shishikura, we prove this conjecture for the restriction of Upsilon to a class of high type numbers.
Date Issued
2015-11-01
Date Acceptance
2014-12-14
Citation
Inventiones Mathematicae, 2015, 202, pp.677-742
ISSN
0020-9910
Publisher
Springer Verlag
Start Page
677
End Page
742
Journal / Book Title
Inventiones Mathematicae
Volume
202
Copyright Statement
© 2015, Springer-Verlag Berlin Heidelberg. The final publication is available at Springer via http://dx.doi.org/10.1007/s00222-014-0576-2
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://arxiv.org/abs/1210.5384v2
Grant Number
EP/M01746X/1
Subjects
math.DS
math.DS
math-ph
math.MP
37F25 (Primary) 58D25 (Secondary)
Notes
66 pages,
Publication Status
Published
Date Publish Online
2015-01-13